Intensity Of Electromagnetic Wave Formula

Power transferred per unit area

In physics, the intensity or flux of radiant energy is the power transferred per unit area, where the surface area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI organisation, it has units watts per square metre (W/grand²), or kg⋅due south⁻³ in base units. Intensity is used most oftentimes with waves such equally acoustic waves (sound) or electromagnetic waves such as light or radio waves, in which instance the average power transfer over one period of the moving ridge is used. Intensity can be practical to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried past drops of h2o from a garden sprinkler.

The word "intensity" every bit used hither is not synonymous with "forcefulness", "amplitude", "magnitude", or "level", every bit it sometimes is in colloquial speech.

Intensity tin be found by taking the energy density (energy per unit volume) at a point in infinite and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of ability divided by area (i.east., surface power density).

Mathematical description [edit]

If a point source is radiating free energy in all directions (producing a spherical wave), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to the altitude from the object squared. This is an example of the inverse-square law.

Applying the law of conservation of energy, if the internet power emanating is constant,

P=\int \mathbf {I} \,\cdot d\mathbf {A} ,

where P is the cyberspace power radiated, I is the intensity vector every bit a function of position, the magnitude $| I |$ is the intensity equally a function of position, and d A is a differential element of a closed surface that contains the source.

If one integrates a uniform intensity, $| I | = constant$ , over a surface that is perpendicular to the intensity vector, for case over a sphere centered around the indicate source, the equation becomes

P=|I|\cdot A_{\mathrm {surf} }=|I|\cdot iv\pi r^{2}\,,

where | I | is the intensity at the surface of the sphere, r is the radius of the sphere, and $A_{\mathrm {surf} }=4\pi r^{ii}$ is the expression for the surface area of a sphere.

Solving for | I | gives

|I|={\frac {P}{A_{\mathrm {surf} }}}={\frac {P}{iv\pi r^{2}}}.

If the medium is damped, then the intensity drops off more chop-chop than the above equation suggests.

Anything that tin transmit energy can have an intensity associated with it. For a monochromatic propagating electromagnetic moving ridge, such as a airplane moving ridge or a Gaussian axle, if E is the complex amplitude of the electrical field, then the time-averaged energy density of the moving ridge, travelling in a non-magnetic material, is given past:

\left\langle U\correct\rangle ={\frac {n^{2}\varepsilon _{0}}{2}}|E|^{2},

and the local intensity is obtained by multiplying this expression past the wave velocity, c/north:

I={\frac {\mathrm {c} n\varepsilon _{0}}{2}}|E|^{2},

where due north is the refractive index, c is the speed of light in vacuum and $\varepsilon _{0}$ is the vacuum permittivity.

For not-monochromatic waves, the intensity contributions of different spectral components tin can but be added. The treatment above does not hold for arbitrary electromagnetic fields. For example, an evanescent wave may have a finite electric amplitude while non transferring whatever power. The intensity should then be defined equally the magnitude of the Poynting vector.^[1]

Alternative definitions [edit]

In photometry and radiometry intensity has a unlike meaning: information technology is the luminous or radiant power per unit solid angle. This can crusade confusion in optics, where intensity can mean whatever of radiant intensity, luminous intensity or irradiance, depending on the groundwork of the person using the term. Radiance is also sometimes called intensity, especially by astronomers and astrophysicists, and in oestrus transfer.

References [edit]

^ Paschotta, Rüdiger. "Optical Intensity". Encyclopedia of Laser Physics and Engineering. RP Photonics.